I have proposed RBFNN-PSO model for Prediction of Sediment Transport at the Limit of Deposition in a Clean Pipe. Do RBFNN-PSO model works with Non-normalized Data?
If you want to be able to make a sensible conclusion you MUST normalize.
This topic has been covered and some nice and interesting answers have already been given on researchgate. You will be able to find them easily if you search the questions/answers with the right keywords (ANN, normalization). Sorry I don't have myself the time to actually do that search and point you to the interesting threads.
Linear normalization mostly support in a homogeneous type of data set to be input to NN. Furthermore, the normalization will make your algorithm faster. Normalized Radial Functions with similar variances (for input variables) may also allow the NN weights to play their rule more firmly.
Definitely ANN works on non-normalized data but the range of variations in data need not be much high. e.g. you can fuzzify 190, 170, 189, 178, 16, 165 heights of students in cm to tall fuzzy set with trapezoidal membership function without doing the normalization on the given data.